# Re-writing formula

• Jun 19th 2010, 08:17 AM
Yvginkel
Re-writing formula
I'm trying to re-write the dividend-discount formula below so that rdiv is the result of the formula. tx is limited to x=3.

Attachment 17921

I'm stuck at:
dps1 - (dps3/r^3) = (P0 - P3)(r-1)

• Jun 20th 2010, 03:05 AM
SpringFan25
are you sure thats the right formula? The denominator in your sum appears to be applying the same discount factor to all dividends, even though they happen at different times.

I think the formula you want is:
$\displaystyle \displaystyle P_0 = \left( \sum \frac{dps_t}{r_{div}^t} \right) + \frac{P_{t_x}}{r_{div}^{t_x}}$

whichever formula you use, provided $\displaystyle r_{div}$ is constant you can write $\displaystyle s=\frac{1}{r_{div}}$. You may be able to factorise depending on the values of $\displaystyle dps_t$ and $\displaystyle P_{t_x}$. Otherwise you have a cubic in s to solve, time to find a computer...
• Jun 20th 2010, 05:30 AM
Yvginkel
Sorry, you're right it should be $\displaystyle \displaystyle P_0 = \left( \sum \frac{dps_t}{r_{div}^t} \right) + \frac{P_{t_x}}{r_{div}^{t_x}}$

Where:
$\displaystyle {r_{div}}$ is constant;
the sum is maxed for 3 periods; and
x = 3

Hence $\displaystyle s=\frac{1}{r_{div}}$ won't work as the sum has only three periods.

I got to $\displaystyle {dps_1} - \frac{dps_3}{r_{div}^3} = ({P_0}-{P_3})(r-1)$ by eliminating $\displaystyle {dps_2}$ and $\displaystyle {dps_3}$.